Let $a$ and $b$ be the solutions of the equation $2x^2+6x-14=0$. What is the value of $(2a-3)(4b-6)$?
Solution: Expanding the desired expression, we get $(2a-3)(4b-6)=8ab-12a-12b+18=8ab-12(a+b)+18$. This implies that we need the sum and product of the roots of the given equation, which are $-6/2=-3$ and $-14/2=-7$, respectively. Thus, the desired expression equals $(8\cdot -7) - (12 \cdot -3) + 18 = \boxed{-2}$.